That a ball rolling inside a spherical bowl undergoes simple harmonic motion for small displacements is a standard classical mechanics result derivable from the equations of motion and energy conservation, requiring no specific citation.
The claim states a foundational physics principle: a ball rolling in a spherical bowl executes simple harmonic motion under small amplitude approximations. This is a matter of basic physics (common knowledge derived from analytical mechanics), and while general concepts of oscillators appear in the literature, specific empirical verification papers are unnecessary for textbook physics derivations. Paper [9] touches on simple harmonic motion and oscillators conceptually.